skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Optimization and large scale computation of an entropy-based moment closure

Journal Article · · Journal of Computational Physics
 [1];  [2];  [2]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States); Univ. of Tennessee, Knoxville, TN (United States)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
+ Show Author Affiliations

We present computational advances and results in the implementation of an entropy-based moment closure, MN, in the context of linear kinetic equations, with an emphasis on heterogeneous and large-scale computing platforms. Entropy-based closures are known in several cases to yield more accurate results than closures based on standard spectral approximations, such as PN, but the computational cost is generally much higher and often prohibitive. Several optimizations are introduced to improve the performance of entropy-based algorithms over previous implementations. These optimizations include the use of GPU acceleration and the exploitation of the mathematical properties of spherical harmonics, which are used as test functions in the moment formulation. To test the emerging high-performance computing paradigm of communication bound simulations, we present timing results at the largest computational scales currently available. Lastly, these results show, in particular, load balancing issues in scaling the MN algorithm that do not appear for the PN algorithm. We also observe that in weak scaling tests, the ratio in time to solution of MN to PN decreases.

Research Organization:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
Sponsoring Organization:
USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC)
Grant/Contract Number:
AC05-00OR22725
OSTI ID:
1261246
Alternate ID(s):
OSTI ID: 1247046
Journal Information:
Journal of Computational Physics, Vol. 302, Issue C; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 17 works
Citation information provided by
Web of Science

References (26)

High-Order Entropy-Based Closures for Linear Transport in Slab Geometry II: A Computational Study of the Optimization Problem journal January 2012
Adaptive change of basis in entropy-based moment closures for linear kinetic equations journal February 2014
Numerical integration on the sphere journal January 1982
Numerical Methods for Balance Laws with Space Dependent Flux: Application to Radiotherapy Dose Calculation journal November 2011
One-dimensional Riemann solvers and the maximum entropy closure journal June 2001
Angular moment model for the Fokker-Planck equation journal July 2010
A deterministic partial differential equation model for dose calculation in electron radiotherapy journal June 2010
A Comparison of Moment Closures for Linear Kinetic Transport Equations: The Line Source Benchmark journal September 2013
Analysis of theM1model: Well-posedness and diffusion asymptotics journal June 2013
Towards physically realizable and hyperbolic moment closures for kinetic theory journal November 2009
On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws journal January 1983
High-order entropy-based closures for linear transport in slab geometry journal January 2011
Convex Duality and Entropy-Based Moment Closures: Characterizing Degenerate Densities journal January 2008
Some properties of the coupling coefficients of real spherical harmonics and their relation to Gaunt coefficients journal September 1996
Maximum Entropy for Reduced Moment Problems journal October 2000
Quadratures on a sphere journal January 1976
Spherical quadrature formulas exact to orders 25?29 journal January 1977
Moment closure hierarchies for kinetic theories journal June 1996
HERACLES: a three-dimensional radiation hydrodynamics code journal January 2007
Affordable robust moment closures for CFD based on the maximum-entropy hierarchy journal October 2013
Effect of the plasma-generated magnetic field on relativistic electron transport journal July 2011
Boltzmann Type Schemes for Gas Dynamics and the Entropy Property journal December 1990
Second-Order Boltzmann Schemes for Compressible Euler Equations in One and Two Space Dimensions journal February 1992
Efficient Storage Scheme for Precalculated Wigner 3j, 6j and Gaunt Coefficients journal January 2004
Entropic approximation in kinetic theory journal May 2004
Hyperbolic Problems: Theory, Numerics and Applications, Part 2: Contributed Talks book January 2009

Cited By (2)

A new entropy-variable-based discretization method for minimum entropy moment approximations of linear kinetic equations journal November 2021
A structure-preserving surrogate model for the closure of the moment system of the Boltzmann equation using convex deep neural networks text January 2021

Similar Records

Efficient algorithms and implementations of entropy-based moment closures for rarefied gases
Journal Article · Sat Jul 01 00:00:00 EDT 2017 · Journal of Computational Physics · OSTI ID:1261246
High-order entropy-based closures for linear transport in slab geometry II: A computational study of the optimization problem
Journal Article · Sun Jan 01 00:00:00 EST 2012 · SIAM Journal on Scientific Computing · OSTI ID:1261246
Data-driven, structure-preserving approximations to entropy-based moment closures for kinetic equations
Journal Article · Fri Mar 24 00:00:00 EDT 2023 · Communications in Mathematical Sciences · OSTI ID:1261246

Related Subjects

97 MATHEMATICS AND COMPUTING
kinetic equations
moment methods
GPU computing
spherical harmonics
high performance computing